definability in logic and rough set theory 1

Tuan Fang Fan; Churn Jung Liau; Duen-Ren Liu

doi:10.3233/978-1-58603-891-5-749

definability in logic and rough set theory ¹

Tuan Fang Fan, Churn Jung Liau, Duen-Ren Liu

Institute of Information Management

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

2 Scopus citations

Abstract

Rough set theory is an effective tool for data mining. According to the theory, a concept is definable if it can be written as a Boolean combination of equivalence classes induced from classification attributes. On the other hand, definability in logic has been explicated by Beth’s theorem. In this paper, we propose two data representation formalisms, called first-order data logic (FODL) and attribute value-sorted logic (AVSL), respectively. Based on these logics, we explore the relationship between logical definability and rough set definability.

Original language	English
Title of host publication	Frontiers in Artificial Intelligence and Applications
Publisher	IOS Press
Pages	749-750
Number of pages	2
ISBN (Print)	978158603891
DOIs	https://doi.org/10.3233/978-1-58603-891-5-749
State	Published - Jun 2008
Event	18th European Conference on Artificial Intelligence, ECAI 2008 - Patras, Greece Duration: 21 Jul 2008 → 25 Jul 2008

Publication series

Name	Frontiers in Artificial Intelligence and Applications
Volume	178
ISSN (Print)	0922-6389
ISSN (Electronic)	1879-8314

Conference

Conference	18th European Conference on Artificial Intelligence, ECAI 2008
Country/Territory	Greece
City	Patras
Period	21/07/08 → 25/07/08

Access to Document

10.3233/978-1-58603-891-5-749

Cite this

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title = "definability in logic and rough set theory 1",

abstract = "Rough set theory is an effective tool for data mining. According to the theory, a concept is definable if it can be written as a Boolean combination of equivalence classes induced from classification attributes. On the other hand, definability in logic has been explicated by Beth{\textquoteright}s theorem. In this paper, we propose two data representation formalisms, called first-order data logic (FODL) and attribute value-sorted logic (AVSL), respectively. Based on these logics, we explore the relationship between logical definability and rough set definability.",

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AB - Rough set theory is an effective tool for data mining. According to the theory, a concept is definable if it can be written as a Boolean combination of equivalence classes induced from classification attributes. On the other hand, definability in logic has been explicated by Beth’s theorem. In this paper, we propose two data representation formalisms, called first-order data logic (FODL) and attribute value-sorted logic (AVSL), respectively. Based on these logics, we explore the relationship between logical definability and rough set definability.

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